... and now Garmin Support response I got today morning
As mentioned - there was around 2-3 hours delay and then more 5-6-10 hours delay before notifications came up on my mobile.
Garmin proposed to disconnect and connect accounts - a friend of mine tried that (without knowing garming recommendation) - and it fixed the issue in his case.
PS: In general - I'd say both support divisions worked fine, keeping in mind it was a weekend.
Thank you for contacting Garmin Europe.
In regards to your data not properly transferring to Strava; I can confirm that we do occasionally see delayed synchronization between the services, especially during periods where the upload volume is especially high.
Whilst activities uploaded to Garmin Connect usually appear in Strava within minutes, sometimes it may take up to 12 hours for an activity to be ported across. We are working with Strava in order to make sure that these delays are minimised for now and prevented completely in the future.
If your data is failing to transfer from Garmin Connect to Strava, I would suggest disconnecting and then re-associating the accounts.
To disconnect your Garmin Connect account from within Strava:
Log in to your Strava account
Go to strava.com/settings/profile
Find Garmin Connect on the right hand side and click "Disconnect
You will also need to disconnect your accounts from Garmin Connect.
To remove the account access permissions in Garmin Connect:
Sign in to Garmin Connect
Select user icon
Select Settings
Select Account Information
Click “Remove Permission” under Applications
Once you have removed the account link from both Strava and Garmin Connect, you can re-associate the accounts by following these steps:
Log in to your Strava account
Go to http://www.strava.com/upload/device Under the Garmin logo, click "Get Started"
Choose "Connect with Garmin"
Enter your Garmin Connect log in credentials to authorize the link to Strava
Once the connection between the accounts has been established, any activities uploaded to Garmin Connect should automatically sync with Strava within minutes. There is no need to wait on the upload page; the new activities will appear automatically. After your first upload, activities in Garmin Connect from the last 30 days will be sent to Strava.​
I'm wondering if this is related to a segment problem in Garmin Connect. Although working correctly on Saturday, 7/30/16, on Sunday, 7/31/16, all the segments in the Segment Leaderboard disappeared from Garmin Connect on the web and on the iPhone. I suspect that Garmin, itself, is not calculating the segments and segment leaderboard but that it is provided by some agreement and interface with Strava. If Strava is having difficulties, then Garmin's access to and use of Strava's segment database might be compromised. I certainly hope they - either Garmin or Strava - get it fixed.